Answered: x2 – 16 This Graph of f(x) = %3D x – 4…

Math

Calculus

x2 – 16 This Graph of f(x) = %3D x – 4 4, but the function is undefined at x = limit as x → 4 exists.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

x2 – 16
This
Graph of f(x) =
%3D
x – 4
4, but the
function is undefined at x =
limit as x → 4 exists.

Expert Solution

Step 1

Given function is $f (x) = \frac{x^{2} - 16}{x - 4}$ .

We know that a rational function is defined if it's denominator is not equal to zero.

So, given function is defined if:

$x - 4 \neq 0 \Rightarrow x \neq 4$

Now, limit of a function $f (x)$ exists at $x = a$ if:

$\lim_{x \to a^{-}} f (x) = \lim_{x \to a^{+}} f (x)$

Step by step

Solved in 2 steps

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